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The Method Man
January 3, 2014 3:45 PM   Subscribe

"700 years ago, a monk needed parchment for a new prayer book. He pulled the copy of Archimedes' book off the shelf, cut the pages in half, rotated them 90 degrees, and scraped the surface to remove the ink, creating a palimpsest—fresh writing material made by clearing away older text. Then he wrote his prayers on the nearly-clean pages." - A Prayer for Archimedes
posted by anastasiav (43 comments total) 23 users marked this as a favorite

 


There are a number of these recent discoveries (like the antikythera mechanism) which seem to pose something of a puzzle no so much by their existence as by their lack of sequelae. If Archimedes was so close to figuring out the calculus, why did no one pick up that ball and run with it during the many centuries before his work was lost?
posted by yoink at 3:53 PM on January 3


Palimpsests and old manuscripts are awesome.

At some point a few years ago, my husband and our roommate were taking the Metro together when a guy came up to them and said "Can I ask you two a question?" They felt a little uncomfortable about being approached this way and assumed the man was going to ask them if they were gay and weren't really sure how to respond to all this but one of them said, "Um, sure", so the guy asked "Are you two...nerds?". Since they were coming back from a museum exhibition on palimpsests and marginalia they felt compelled to answer yes.
posted by Mrs. Pterodactyl at 3:53 PM on January 3 [19 favorites]


If Archimedes was so close to figuring out the calculus, why did no one pick up that ball and run with it during the many centuries before his work was lost?

Someone disturbed the circles.
posted by uosuaq at 3:59 PM on January 3 [10 favorites]


Is there any definition of barbarism more complete than wiping out knowledge to replace it with superstition? I'm glad that this has been rediscovered, but the notion that anyone would vandalize a book on mathematics by one of the greatest minds of the ancient world is repulsive.
posted by 1adam12 at 4:00 PM on January 3 [5 favorites]


In this case, it did work, but it remained for Newton and Leibniz to figure out how to make the argument mathematically rigorous.

I think it took longer than that to make it "rigorous", like until the 19th Century.
posted by thelonius at 4:00 PM on January 3 [1 favorite]


Is there any definition of barbarism more complete than wiping out knowledge to replace it with superstition?

Well, to be fair to a long dead monk, it's possible that he had no idea that the work was so rare (it may not have been a unique text at the time he reused it); it's possible, indeed, that he had no idea what the text was. Parchment was expensive stuff and reuse was very common.
posted by yoink at 4:08 PM on January 3 [16 favorites]


Think of what we do to books in the name of set decoration.
posted by maryr at 4:20 PM on January 3 [4 favorites]


Mrs. Pterodactyl, why on earth did the guy on the subway need to verify that your husband was a nerd?
posted by maryr at 4:22 PM on January 3 [1 favorite]


Nerd Census. Important for figuring out nerd taxes and the like.
posted by wemayfreeze at 4:25 PM on January 3 [13 favorites]


This mostly sounds like it's describing the Method of Exhaustion, which is conventionally analogized to calculus and didn't originate with Archimedes, though perhaps there wasn't previously evidence of it being applied to a parabola in that era. If this restoration and analysis of the text is getting obscured fragments of manuscript into the hands of historians, that's awesome, but the implication that the research has revealed something completely novel and closer to calculus than was known of before is probably just science journalism either being its usual sensationalizing self or unquestioningly passing on the claims of a press release.
posted by XMLicious at 4:27 PM on January 3 [1 favorite]


"Are you two...nerds?"

I very much hope this once again becomes a situation with further hilarious followup from the Mr.
posted by elizardbits at 4:31 PM on January 3


Even if Archimedes did discover integrals, I bet the English would still say that Newton was first.
posted by thelonius at 4:32 PM on January 3 [4 favorites]


If Archimedes was so close to figuring out the calculus, why did no one pick up that ball and run with it during the many centuries before his work was lost?

Good question, I'll take a shot at it

The things that calculus actually lets you do (calculate volumes, areas, or in the other direction, rates of change etc) are very useful for engineering. But in the era that Archimedes lived, there were probably far fewer applications. It would have been a lot more abstract. That is, figuring out the exact volume of a 3D shape became a lot more useful around the industrial revolution than it did around Archimedes time.

Also, just problems around books, education, literacy, and the flow of information.
posted by memebake at 4:35 PM on January 3 [1 favorite]


Think of what we do to books in the name of set decoration.

I'm a pretty nerdy dude, have an English Lit degree, I love to read and I used to have a pretty extensive book collection. I'm also a stagehand and worked for years decorating sets for the soaps. In all that time, in all those libraries, I never saw one book that was worth much. And I kept my eye out. They used to buy them in 100 lb lots.
posted by nevercalm at 4:35 PM on January 3 [4 favorites]


This mostly sounds like it's describing the Method of Exhaustion,

Except that that method doesn't admit of "actual infinity." That's the part of this which the article is claiming to be new, not the method of approximating to an arbitrary degree of exactitude (i.e. "potential infinity.")
posted by yoink at 4:38 PM on January 3 [1 favorite]


though perhaps there wasn't previously evidence of it being applied to a parabola in that era

The article linked here doesn't make it clear, but Archimedes' computation of the area of a parabolic segment using the method of exhaustion (as well as by a method using his theory of levers) is in The Quadrature of the Parabola, which we've had forever — here's Heath's 1897 translation into English. This isn't one of the texts recovered from the palimpsest.
posted by stebulus at 4:50 PM on January 3 [1 favorite]


Progress isn't inevitable. They had the steam engine, too. Sometimes an important piece is missing. I imagine that not having the Arabic numeral system and algebra was fairly crippling for taking geometry into proper calculus.
posted by empath at 4:59 PM on January 3 [4 favorites]


But in the era that Archimedes lived, there were probably far fewer applications.

I once read a very fine SF short story, which I can't begin to locate now, about a time traveller who thought the thing to do was go back and encourage the Greek philosophers to finish pursuing their craft. Instead he convinced them that their craft had been pursued to completion elsewhere, so they went on to more spiritual pursuits because they didn't value math for practical applications. So Archimedes might have worked out the Calculus, but it never would have occurred to him to use it to build something; that was crass engineering fit for slaves and mundanes.

In fact, the way mathematical truths were treated by the Greeks is in some ways remniscent of how less obviously useful occult knowledge was treated by more modern groups like the Catholic Church or the OTO. If you are keeping the existence of the dodecahedron a sacred secret it's unlikely you're going to reveal your insights to the people most likely to be able to turn them into a higher standard of living.
posted by localroger at 5:16 PM on January 3 [2 favorites]


But Archimedes did not at all consider himself above engineering; he built various clever devices to defend Syracuse against a Roman siege.
posted by thelonius at 5:34 PM on January 3 [5 favorites]


Except that that method doesn't admit of "actual infinity." That's the part of this which the article is claiming to be new, not the method of approximating to an arbitrary degree of exactitude (i.e. "potential infinity.")

I see what you're saying, you're right. I think I'd skimmed past that aspect of it too quickly when their expert noted that the text's argument is "definitely not completely valid" and the article went on to note that "actual infinity" isn't used in modern calculus, anyways. Maybe those details are the answer to your question about why this work by Archimedes wasn't expanded upon?

Regardless of whether this really means he had his foot on the threshold of calculus, it does kind of lend verisimilitude to the eureka story, so that's cool.
posted by XMLicious at 5:54 PM on January 3


the notion that anyone would vandalize a book on mathematics by one of the greatest minds of the ancient world is repulsive.

700 years ago, it probably wasn't the only copy in existence. The monk may even have had two copies and decided to recycle one.
posted by charlie don't surf at 5:55 PM on January 3 [4 favorites]


Is there any definition of barbarism more complete than wiping out knowledge to replace it with superstition? I'm glad that this has been rediscovered, but the notion that anyone would vandalize a book on mathematics by one of the greatest minds of the ancient world is repulsive.

We live in different ages and different times, and to imply a level of barbarism for our poor unnamed monk who we are now separated 700 years from is extremely arrogant. We don't know what he had in his library already, as many have pointed out. The prayers that he wrote down, if they were some sort of singular poetry, if they were a work of art that humanity would come to cherish hundreds of years from now, would it still be barbaric to create it?

As much as we like ascribe thoughts of Progress and Barbarism to history, the messy individual lives and the cultural contexts are too complicated and powerful to wipe them away to create that narrative. If this book wasn't "vandalized", perhaps very little, if anything would have changed in the sweep of knowledge and progress.

Think about everything you throw away, everything you delete on a daily basis, everything you forget or don't do your utmost to preserve. I hope that 700 years from now, the future forgives us for destroying that which is important to them.
posted by Lord Chancellor at 6:10 PM on January 3 [9 favorites]


Also, the article notes that we're talking about something written on parchment rather than paper, which is the only reason it still exists, right? Maybe there had just been a pre-moveable-type printing run of the Archimedes work on paper and so it appeared fairly common from the monk's perspective, but those all crumbled to dust a long time ago.
posted by XMLicious at 6:17 PM on January 3


But Archimedes did not at all consider himself above engineering; he built various clever devices to defend Syracuse against a Roman siege.

I have no idea how reliable it is, but there's a bit in Plutarch's Marcellus about Archimedes' attitude to engineering:
Yet Archimedes possessed so high a spirit, so profound a soul, and such treasures of scientific knowledge, that though these inventions [the weapons used to defend Syracuse] had now obtained him the renown of more than human sagacity, he yet would not deign to leave behind him any commentary or writing on such subjects; but, repudiating as sordid and ignoble the whole trade of engineering, and every sort of art that lends itself to mere use and profit, he placed his whole affection and ambition in those purer speculations where there can be no reference to the vulgar needs of life; studies, the superiority of which to all others is unquestioned, and in which the only doubt can be whether the beauty and grandeur of the subjects examined, of the precision and cogency of the methods and means of proof, most deserve our admiration.
This is after a previous bit about the cultural context:
Eudoxus and Archytas had been the first originators of this far-famed and highly-prized art of mechanics, which they employed as an elegant illustration of geometrical truths, and as means of sustaining experimentally, to the satisfaction of the senses, conclusions too intricate for proof by words and diagrams. As, for example, to solve the problem, so often required in constructing geometrical figures, given the two extremes, to find the two mean lines of a proportion, both these mathematicians had recourse to the aid of instruments, adapting to their purpose certain curves and sections of lines. But what with Plato's indignation at it, and his invectives against it as the mere corruption and annihilation of the one good of geometry, which was thus shamefully turning its back upon the unembodied objects of pure intelligence to recur to sensation, and to ask help (not to be obtained without base supervisions and depravation) from matter; so it was that mechanics came to be separated from geometry, and, repudiated and neglected by philosophers, took its place as a military art.
posted by stebulus at 6:30 PM on January 3 [9 favorites]


Very interesting! Perhaps he felt that he had to put aside his preferences and do what he could to help the defense.
posted by thelonius at 6:33 PM on January 3


Yeah, that would make sense. Or maybe this is just Plutarch guessing at Archimedes' motives for not writing about the technology?
posted by stebulus at 7:09 PM on January 3


Also, the article notes that we're talking about something written on parchment rather than paper, which is the only reason it still exists, right?

No, paper is quite durable and high quality paper can last thousands of years. There are paper documents far older than that pallimpsest. Just briefly poking around my own scholarly field, this list of ancient Japanese documents has well preserved paper specimens dated as far back as 749 AD. I have personally seen Chinese paper documents in a museum claimed to date back to 200 BC but I am skeptical.
posted by charlie don't surf at 7:40 PM on January 3 [1 favorite]


Lots of people, including Euclid, Archimedes, Oresme, Napier, and Descartes(as well as chinese, japanese, indian, and arabic mathematicians) had pieces of the calculus. Many of which were quite generalizable. What Newton, Leibniz, and Seki Takakazu did wasn't really inventing the calculus. What they did was systematize it. They invented notation and found rules that made the calculus much easier to do and teach. Instead of doing everything by scratch every single time, the introduced tools like the power rule and the product rule and the notation to support them. What they did was make calculus easy enough that it could be recognized as a "thing." and when it became a thing, it was discovered.

Why not earlier? paper has a lot to do with it. Paper has existed for a long time, but it wasn't until after the plague that paper became cheap. Cheap paper means things like palimsests were no longer necessary. Mathematicians had much more freedom to play with symbols, and algebra exploded as a result (ex: Cardano). with the freedom to play with symbols and the increasing abstraction of mathematics came the freedom to create notations like Newton and Leibniz' (both of which are still used, but in different fields)

So Newton, Leibniz, and Takakazu did not invent calculus, it's more acurate to say they invented the notatitions that allowed them to discover the underlying ideas of calculus that people had been using for thousands of years but never really reified until the 1600s. One might even say that what they did was stand on the shoulders of giants to see just a little farther.

They also didn't formalize the calculus. That was hundreds of years later with the works of cauchy, dedekind, dirchlet, lesbegue, and ultimately the bourbakis. (and robinson, if you count the formalization of the infinitesimal, which I do).

iPad post. sorry for typos.
posted by yeolcoatl at 8:05 PM on January 3 [9 favorites]


also, newton and leibnitz's approaches relied heavily on coordinate geometry, so descartes sort of had to happen first. not sure about takakazu's approach. That's harder to get a hold of in the U.S.
posted by yeolcoatl at 8:10 PM on January 3


the guy asked "Are you two...nerds?"

"Do you know my friend Steve? He's a nerd."
posted by Ray Walston, Luck Dragon at 8:28 PM on January 3 [1 favorite]


yoink: "If Archimedes was so close to figuring out the calculus, why did no one pick up that ball and run with it during the many centuries before his work was lost?"

I find it indicative of a pervasive bias that when the Greco-Romans failed to advance to a teleogically satisfactory degree after several hundred years of regional hegemony, it's a mystery, yet when a similar pattern is described applying to the Arab-Hiberno-Persian civilisation, people like Bertrand Russell and his spiritual descendents deploy it in service to the idea of the Lassitudinous Oriental. I don't think that the emergence of Christianity as the Rome's state religion in Rome created a Dark Age, nor was it necessarily a signifier of a "turn" away from inquiry. Similarly I don't think that the identification of Islam as the state religion of the Arabic-Hiberno-Persians necessarily caused that civilisation to fail to progress. As with the Greco-Indian, the Indian, the Egyptian, the Chinese, the Oba, the Maya, etc, they reached a state of dynamic equilibrium, culturally persisting against both internal and external disruptors and occasionally enabling constrained outbreaks of scientific development. It was the turn towards international trade and the ongoing labor disruptions of mass slavery and then fossil fuel exploitation that created this globalised natural selection and a historically atypical Modern system of sustained scientific effort that has persisted for several hundred years. Also, a stable climate helped.

Roughly around that same time that some unnamed person was scraping off archaic lettering to make way for religious writing, Ibn al-Nafis was correcting Galen and describing the pulmonary circulation. He was also busy writing on opthalmology and optics, and penning an apocalyptic SF novel with many themes later taken up by Voltaire in Candide. In the Arab-Hiberno-Persian civilisation, this kind of positivism and polymath activity resembling Enlightenment Euro culture was not unusual for educated men there. Why did it come to an end? Why did it take the Europeans another 400 years for Harvey to come along and describe pulmonism all over again? al-Nafis's civilisation was already in retreat, facing an existential crisis squeezed between the Christians and the Mongols. The Battle of Baghdad in the middle of the 13th century basically annihilated the world's most economically advanced and prosperous city and its library while eliminating the Abbasid state. It was a massively destabilising blow to progress in the region, as much as the destruction of Rome or Alexandria were in their day. In the ordinary course of events, you might have expected congruent progress to re-commence relatively quickly, in a colocated or nearby successor state, but then the 14th century happened, first with climate disasters and then with pandemics. That bollixed things up for longer than expected.

We're just relatively lucky in that our progress centres are more decentralised now. We can lose entire cities to war or disaster, such as Berlin or Lisbon, and there are more left to continue. Our ancestors did not have this networked resilience or simple massive surplus of people.
posted by meehawl at 9:34 PM on January 3 [6 favorites]


It was the turn towards international trade and the ongoing labor disruptions of mass slavery and then fossil fuel exploitation that created this globalised natural selection and a historically atypical Modern system of sustained scientific effort that has persisted for several hundred years.

Yes, if only Greco-Roman civilization had international trade and mass slavery, think how different history might have been.

Also, um, Arab-Hiberno-Persian? Does Ireland have a proud but little-know history as an Islamic Emirate?
posted by strangely stunted trees at 10:05 PM on January 3 [1 favorite]


Maybe he meant Arab-Hispano (or Ibero)-Persian?

Though I had a sudden image of the monks who illustrated the Book of Kells having a high old time hanging out in Baghdad!
posted by suburbanbeatnik at 10:44 PM on January 3


I'm a librarian that loves old books and the knowledge they contain. I recently heard about a monk that was transcribing old parchments. He was concerned about errors caused by so many copies of copies through the years so he went into the stacks to source the original material. I hear the other monks found him, hours later, crying hysterically: "it said celebrate..."
posted by saucysault at 11:27 PM on January 3 [2 favorites]


when the Greco-Romans failed to advance to a teleogically satisfactory degree

It always drove me mad how people would just teach the "Pre-Socratic" philosophers as kind of defective natural scientists and move on. I don't want to go full Heidegger, but I think they were doing some kind of thinking that has no exact analogy in our culture now.
posted by thelonius at 12:41 AM on January 4 [3 favorites]


Or maybe this is just Plutarch guessing at Archimedes' motives for not writing about the technology?

After a night's sleep, I think this is what it most looks like. You could easily tell a story where Plutarch wants to amaze his readers with the achievements of an intellectual giant of centuries past, but is well aware of the denigration of mechanics by high-minded philosophers and doesn't want readers thinking poorly of Archimedes because of that prejudice. The way he tells the story, he gets to have it both ways: Archimedes' mechanical achievements are evidence for his being supersmart, while his putative turning away from them are evidence of his high moral character. (It reminds me of that bit in To Kill a Mockingbird where Atticus kills the rabid dog — he's "the best shot in the county" but "hasn't shot a gun in years", which positions the character as high status by the standards of two (sub)cultures at once.)
posted by stebulus at 7:12 AM on January 4 [1 favorite]


Basically, what yeolcoatl said.

But my understanding was that a major part of the puzzle brought by Leibniz and the filthy English plagiarizer was the fundamental theorem of calculus. The work on finding volumes and areas had already existed in pieces, scattered here and there, as had a number of pieces on rates of change. Putting them together and seeing that derivatives and integrals were (kind of) inverse operations was the big innovation. That, and creating lots of notation and general frameworks.
posted by kaibutsu at 8:11 AM on January 4 [3 favorites]


We live in different ages and different times, and to imply a level of barbarism for our poor unnamed monk who we are now separated 700 years from is extremely arrogant.

I am comfortable behind arrogant towards a monk from 700's ago. The monk may or may not have had personal animosity against the Classical underpinnings that make up the modern world, but the entire process of a civilization giving up it's birthright was a descent into barbarism.
posted by spaltavian at 9:12 AM on January 4


meehawl: I don't think that the emergence of Christianity as the Rome's state religion in Rome created a Dark Age, nor was it necessarily a signifier of a "turn" away from inquiry. Similarly I don't think that the identification of Islam as the state religion of the Arabic-Hiberno-Persians necessarily caused that civilisation to fail to progress.

These were manifestly different events in these two civilizations, though. Islam was essentially a Arab nationalist revolt, pushing out the influence of Romans and Persians (recently exhausted by a war ending only in 610). It later transmogrified into an imperially-binding ideology. Being Muslim joined you to the state.

Christianity was another Eastern mystery cult that was used cynically by a faction in a civil war; it's institutionalization was also predicated on violence and decreasing accommodation with other (and in some cases, better, creeds). It wasn't used to bind you to the Roman state, it was used to separate people within the Roman state; often the elites.

Economic and demographic changes did far more to undo Roman civilization; of course; the rise of latifundia made a mockery of Roman citizenship and retarded development outside of Italy.

But that, is in part of why people seem surprised by the failure of Romans to achieve modernity; they really seemed to have all the ingredients to make a culture very similar to our own. They had perhaps the first middle class, and in the time of Augustus, wasn't clear that they would be squeezed so hard as to almost disappear. You identify the slave trade as what brought about our modernity, but that missed that modernity was already in progress for sometime before 1492, and well before the Atlantic slave trade was up and running. The Romans already had the other condition you stated, which was international trade. There were Sino-Roman trade missions and trade with India was booming.

The impressive Arab achievements you list were just that, but it's also telling they were re-discoveries of Greco-Roman thought or improvements upon them. The version of Arab civilization would no doubt continued to progress had it not been for the Ilkhanate; perhaps checking European development, but that doesn't mean it would have looked like today's world.

There have been racist or imperialist motives for lamenting Rome and ignoring Baghdad. But the special focus on Rome also comes from the fact that they were really, really close to what we would consider modern. It's just not aesthetics that we took from them. As much as revisionist history is ascendant right now (the Middle Ages were great! Rome didn't even have spurs!) they (and their direct descendants) in Italy really did look more like modern Western civilization than anyone else between 476 and Plutarch.
posted by spaltavian at 9:40 AM on January 4 [1 favorite]


spaltavian: "The impressive Arab achievements you list were just that, but it's also telling they were re-discoveries of Greco-Roman thought or improvements upon them."

I think your framing of 600 years of development as "re-discovery" is quite interesting. It's all a matter of perspective. Were the Romans "re-discovering and improving" on the achievements of the Babylonians? Or the Persians?

I do apologise for the Hiberno/Hispania mixup! Late night!

spaltavian: "The special focus on Rome also comes from the fact that they were really, really close to what we would consider modern ... they (and their direct descendants) in Italy really did look more like modern Western civilization than anyone else between 476 and Plutarch."

I think that's also a matter of perspective. Western Europeans for the most part are descended from the barbarian anti-urbanist cultures that overwhelmed and assimilated the Romans. We have deeply ingrained survivor guilt and survivor envy. To the Roman successor state in the East organized around Byzantium, we were all just uncouth and doctrinally errant "Franks" who eventually sacked Nova Roma in 1204 during the Fourth Crusade. Ignoring the distraction of the shared Latin/Greek languages which we appropriated, Rome both Western and Eastern appear much more "semitic" and similar to the Persian or Islamic Empires than to the Western European proto-states.

The illusion that the Republican and Empire Romans resembled us is selection bias. Early censorship removed or ignored what was alien, foreign or repugnant to the new regimes (as this very thread's example of earlier mathematics being erased in favour of doctrine). Our culture was built on and organised in congruence with the scant fragments that remained. It's only when we read 2nd-hand accounts of the now-erased contemporaneous cultures in things like Against Heresies or Against Celsus that we see how utterly bizarre that era would have seemed to us. Or when we see the murals and common graffitti of Pompeii and encounter people who looked somewhat like us but had radically different mores and worldviews. We can describe something like euergetism in terms of its overt, economic effects but we have no real idea how such an idea survived for so long and was so pervasive and binding to the Idea of Rome and its persistence. To take a future example, in a thousand years, will historians struggle to explain the US's close attachment to a founding constitutional document several hundred years old and its persistence in retaining the structures and words of that document even as the economics and culture of the people enacting it changed dramatically. Western Europeans are not majorly engaged in doctrinal battles over how to square their current politics with the thoughts of late-18th century politicians. In the US, this disagreement seems to be resulting in frequent paralysis of the body politic. To future historians, it may be as describable yet incomprehensible as the red/blue/green/white factional rivalry in late Rome that resulted in Nika Uprising, the greatest disruption to the New Romans' urban fabric before the Frankish Sack of 1204.
posted by meehawl at 12:41 PM on January 4 [1 favorite]


We can describe something like euergetism

Perhaps we can, but apparently Wikipedia can't; that article is surreal.
posted by ogooglebar at 9:34 AM on January 5


Looks like it was machine translated.
posted by empath at 2:31 PM on January 5


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